Abstract: In recent years, researchers have begun investigating
relationships between genomic chromosomal copy number variation and
clinical biomarkers of various diseases. The genomic copy number
profile is a genomic structural measurement of the number of DNA
copies, obtained as a function of genomic location. Clinical
biomarkers are patient-specific serum/blood proteins known to be
associated with prognosis of a disease. The relationships between the
copy number profile and clinical biomarkers are often known to be very
complicated, especially in a heterogeneous disease such as cancer.
Nonlinear methods lend themselves to this complicated relationship. In
this paper, we consider a semiparametric functional model that relates
a continuous outcome to demographic covariates and a functional
covariate of a copy number profile. The functional covariate is modeled
nonparametrically. The estimates of the functional effect of the copy
number profile and the regression coefficients of the demographic
covariates are obtained by establishing a relationship between the
semiparametric functional model and linear mixed models. A score test,
based on the linear mixed model framework, is proposed to test for the
effect of the functional covariate on the continuous response. Using
simulations, we find that our method performs well with respect to
standard functional regression techniques when the true relationship
between the copy number profile and the clinical biomarker is linear.
The performance of our method increases when the relationship between
the copy number 1 profile and the clinical biomarker is nonlinear.
Additionally, the method is illustrated on a Multiple Myeloma data
set. Here, our method identified regions along the copy number profile
that are significantly related to the clinical biomarker Beta-2 Microglobulin.

Title: Smooth Change Point Estimation for the Quantification of Glacier Retreat
Authors: Joe Usset*, Ana-Maria Staicu, Arnab Maity, and Armin Schwartzman

Abstract:  Better tracking of glacial systems would help identify
their relationships with climate change, and improve our ability to
monitor and predict changes in water supply. Numerous studies have
made use of Landsat satellite images to investigate single glaciers of
interest, but to broadly catalog temporal changes worldwide, a robust
and automated methodology is needed. The objective of our work is to
develop a semi-automated way to quantify the retreat of mountain
glaciers from 2-D Landsat satellite images. The method we propose is
to extract 1-D image profiles from the 2-D images, along inlets of the
glaciers, where recession might be noticeable. Within each profile
lies a single glacier terminus – a change point. To find them, we
perform spline smoothing on each profile and focus on inflection
points. The challenge is that many inflection points occur in each
profile, and most are noise. But we have sampled these 1-D profiles
over time. This has allowed us to find a penalization criterion that
integrates information across time points, and estimate glacial
recession as a smooth path of change points. We demonstrate the
effectiveness of our method by application to image data collected on
the Franz Josef, Gorner, Rhone, and Nigardsbreen glaciers.